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<title>Simulations for Statistical and Thermal Physics</title>
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<h3 style="text-align: center;">Java Simulations for Statistical and
Thermal Physics</h3>
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<p>These programs were written for the Statistical and Thermal Physics curriculum development project and  are part of the Open Source Physics project. The programs are released under the GNU General Public License.  The source code is available at &#60;stp.clarku.edu&#62;, where you can run these programs as applets in a browser.</p>

<p>To see the introduction and problems for a topic click on a topic to the left. To run the simulation double click on the topic.</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;The goal of the simulations and calculations is to illustrate some
of the fundamental concepts in statistical mechanics. They can be used
as standalone programs, or in conjunction with a text such as Daniel
Schroeder, <a href="http://physics.weber.edu/thermal/"><i>An Introduction to Thermal Physics,</i></a> Addison-Wesley
(2000), or in conjunction with the online <a href="http://stp.clarku.edu/notes/">notes</a> by Harvey Gould and Jan
Tobochnik.</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;The programs were developed by Kipton Barros, Joshua Gould, Harvey
Gould, Natali Gulbahce, Peter Sibley, Jan Tobochnik, and most recently by Hui Wang and Ranjit Chacko.</p>

<ol>

<li><a href="approachtoequilibrium/index.html"><b>Approach to Equilibrium</b></a>. Explore some of the qualitative properties of macroscopic systems.</li>

<li><a href="demon/index.html"><b>An ideal thermometer</b></a>. Why is an extra degree of freedom called the demon an ideal thermometer?</li>

</ul>
</li>

<li><a href="randomwalks/index.html"><b>Random walks</b></a>. What happens to a drunken sailor?</li>

<li><a href="sensitive/index.html"><b>Sensitivity to initial conditions</b></a>.
A molecular dynamics
simulation of a Lennard-Jones system in a specially prepared state.</li>


<li><a href="numberofstates/index.html"><b>Number of states of a particle in a box</b></a>. A comparison of the actual number of states to the asymptotic expression.</li>

<li><a href="cointoss/index.html"><b>Multiple coin toss</b></a>. Monte
Carlo simulation of the
statistical properties of the outcome of the tosses of many coins. </li>

<li><a href="binomial/index.html"><b>Binomial distribution</b></a>. The plots illustrate how the width and relative width depend on N, the number of steps. </li>

<li><a href="centrallimittheorem/index.html"><b>Central limit theorem</b></a>. A
demonstration of the probability
distribution of a random additive process.</li>

<li><a href="estimate/index.html"><b>Monte Carlo estimation</b></a>.
Estimation of the area under a curve
using the "hit or miss" method.</li>

<li><a href="multiplicativeprocess/index.html"><b>A simple multiplicative random
process</b></a>. The simulation illustrates the importance of rare events.</li>

<li><a href="boltzmann/index.html"><b>Boltzmann probability</b></a>. A
Monte Carlo simulation of an
ideal classical gas in one dimension in equilibrium with a heat bath.</li>

<li><a href="einsteinsolid/index.html"><b>Simple thermal interaction</b></a>.
Calculation of the number of states of two
harmonic solids that can exchange energy.</li>

<li><a href="einsteinsolidheatbath/index.html"><b>Einstein solid at temperature T</b></a>. Simulation of Einstein (harmonic) solid in equilibrium with a heat bath at temperature T using the Metropolis algorithm.</li>

<li><a href="entropy/index.html"><b>Entropy and temperature</b></a>. Calculation of the
entropy of two harmonic
solids that can exchange energy.</li>

<li><a href="thermalcontact/index.html"><b>Thermal equilibrium</b></a>. A
molecular dynamics simulation of
two solids in thermal contact. What quantity becomes the same in
thermal equilibrium?</li>

<li><a href="ljfluid/index.html"><b>Lennard-Jones fluid</b></a>. A molecular
dynamics simulation of a
liquid in two dimensions. Output includes the mean pressure,
temperature, and heat capacity.</li>

<li><a href="harddisks/index.html"><b>Hard disks</b></a>. A molecular
dynamics simulation of hard disks.
Output includes the mean pressure, the mean free path, and the mean collision time.</li>

<li><a href="ising/index.html"><b>The Ising model</b></a>.

<ul>

<li><a href="ising/ising1d.html"><b>1D Ising model</b></a>. A Monte Carlo
simulation of the
one-dimensional Ising model. Output includes mean energy and heat
capacity.</li>

<li><a href="ising/ising2d.html"><b>2D Ising model</b></a>. A Monte Carlo
simulation of the
two-dimensional Ising model. Output includes the mean energy, heat
capacity, and the susceptibility.</li>

<li><a href="ising/antiferromagnet.html"><b>Simulation of the Ising antiferromagnet on a square lattice</b></a>.</li>

<li><a href="ising/triangularlattice.html"><b>Simulation of the Ising antiferromagnet on a triangular lattice</b></a>.</li>

<li><a href="ising/meanfieldsolution.html"><b>Mean-field solution</b></a>. Plot of the numerical solutions to the usual self-consistent equation and the corresponding free energy.</li>

<li><a href="ising/wanglandau.html"><b>Density of states of the 2D Ising
model</b></a>. A Monte Carlo
estimation of the density of states using the Wang-Landau algorithm.</li>

<li><a href="ising/partitionFunction.html"><b>Partition function of the 2D Ising model</b></a>. A Monte Carlo estimate of the partition function using a novel algorithm.</li>

</ul>
</li>

<li><a href="idealgas/index.html"><b>Ideal gas integrals</b></a>

<ul>
<li><a href="idealgas/bosegas.html"><b>Ideal Bose gas</b></a>. Calculation of
the chemical potential as a
function of temperature for fixed density for an ideal Bose gas.</li>

<li><a href="idealgas/fermigas.html"><b>Ideal Fermi gas</b></a>. Calculation
of the chemical potential as
a function of temperature for fixed density. The calculated chemical
potential is used to determine the mean energy.</li>
</ul>
</li>

<li><a href="xymodel/index.html"><b>XY or planar model</b></a>. A
simulation of the two-dimensional XY
model. See the development of vortices below the Kosterlitz-Thouless
transition.</li>

<li><a href="latticedemon/index.html"><b>Generalized demon algorithm</b></a>. A generalization of the demon algorithm that yields the chemical potential as well as the temperature.</li>

<li><a href="isinglatticegas/index.html"><b>Ising lattice gas</b></a>. A simulation of a lattice gas with different chemical potentials.</li>

<li><a href="widom/index.html"><b>Chemical potential</b></a>. An estimation of the chemical potential of a Lennard-Jones fluid using the Widom insertion method</li>

<li><a href="fpu/index.html"><b>Fermi-Pasta-Ulam problem</b></a>.
Simulation of a chain of
oscillators coupled by anharmonic springs.</li>

<li><a href="percolation/index.html"><b>Percolation</b></a>. The nature of
the geometrical phase
transition for site percolation on a square lattice is illustrated.</li>

<li><a href="qmc/index.html"><b>Quantum Monte Carlo</b></a>. A Monte Carlo simulation of an ideal quantum gas in one, two, or three dimensions.</li>

<li><a href="diffusion/index.html"><b>Diffusion in a solid</b></a>. A
simple Monte Carlo simulation of
particles on a lattice with a maximum of one particle per site.</li>

</ol>

<p>The Open Source Physics Java code library is described in Wolfgang
Christian, <i>Open Source Physics: A User's Guide with Examples</i>,
&copy; Addison-Wesley, 2007.</p>

<p class="small">Updated 5 March 2008.</p>

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